Problem 13 · 2016 Math Kangaroo
Stretch
Logic & Word Problems
work-backward
A knock-out tennis tournament is taking place. There are seven matches (4 quarter finals, 2 semi finals and one final). The results for six of the seven matches are known (but not necessarily in this order): Bella beats Ann, Celine beats Donna, Gina beats Holly, Gina beats Celine, Celine beats Bella, Emma beats Farah. Which result is missing?
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Answer: E — Gina beats Emma
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Hint 1 of 2
Eight players, so the four listed wins over Ann, Donna, Holly, Farah are the quarter-finals.
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Hint 2 of 2
Trace who reaches the semi-finals and final to spot the missing match.
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Approach: reconstruct the bracket
- Quarter-final winners are Bella, Celine, Gina, Emma.
- Celine beats Bella and Gina beats Celine (the final), so Gina and Celine reached the final via the semis.
- The other semi-final, Gina over Emma, is the one not listed: Gina beats Emma.
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